In information theory, a low-density parity-check (LDPC) code is an error correcting code for transmitting a message over a noisy transmission channel. LDPC codes are a class of linear block codes. While LDPC and other error correcting codes cannot guarantee perfect transmission, the probability of lost information can be made as small as desired. LDPC was the first code to allow data transmission rates close to the theoretical maximum known as the Shannon Limit. LDPC codes can perform with 0.0045 dB of the Shannon Limit. LDPC was impractical to implement when developed in 1963. Turbo codes, discovered in 1993, became the coding scheme of choice in the late 1990s. Turbo codes are used for applications such as deep-space satellite communications. LDPC requires complex processing but is the most efficient scheme discovered as of 2007. LDPC codes can yield a large minimum distance (hereinafter “dmin”) and reduce decoding complexity.
The IEEE 802.11ad standard (also referred herein as “11ad”) enables communication in frequencies around 60 GHz for very high throughput. The IEEE 802.11ad standard also defines four LDPC matrices, each corresponding to a code rate 1/2, code rate 5/8, code rate 3/4, and code rate 13/16, respectively.